The Dynamic Systems and Control group at UC San Diego integrates, at a fundamental level, system design, modeling, and control disciplines to obtain improved performance of the dynamic response of engineering systems using feedback. As such, the areas of research of the Dynamic Systems and Control group is a joint activity in the topics of systems integration, dynamic system modeling, feedback control design, and the fundamentals of systems theory as applied to linear and nonlinear dynamic systems, mechatronics, structural control, aerospace, and fluid-mechanical systems.
The ability of machine learning techniques to leverage data and process rich sensory inputs (e.g., vision) makes them highly appealing for use in robotic systems. However, the inclusion of learning-based components in the control loop poses an important challenge: how can we guarantee the safety of such systems? For safety, we present a controller synthesis technique based on the computation of reachable sets, using optimal control and game theory.
Automatic control systems are increasingly deployed in unstructured environments featuring novel and dynamically changing conditions. Ensuring successful operation in such scenarios requires revisiting the core problems of stabilization and tracking to impose strict safety constraints.
This talk will cover some of our recent work that enables provable safe control of robots when there are dynamic uncertainties and constraints. The safe control is designed under the framework of energy-function-based methods, where a scalar energy function (also known as barrier function, safety index, etc) needs to be synthesized first such that safe states are with low energy, then the safety controller will be synthesized to dissipate the system energy.
This work describes how machine learning may be used to develop accurate and efficient nonlinear dynamical systems models for complex natural and engineered systems. We explore the sparse identification of nonlinear dynamics (SINDy) algorithm, which identifies a minimal dynamical system model that balances model complexity with accuracy, avoiding overfitting. This approach tends to promote models that are interpretable and generalizable, capturing the essential “physics” of the system. We also discuss the importance of learning effective coordinate systems in which the dynamics may be ex
Koopman operator linearization approximates a nonlinear system of differential equations as a higher-dimensional linear system. This is attractive since many types of analysis, including formal verification using reachability analysis, are significantly more tractable for linear systems.
We present an extension of the linear-quadratic regulator problem to polynomial systems. The resulting feedback control can be written as a solution to the Hamilton-Jacobi-Bellman equations. The Kronecker product structure of the problem found in polynomial systems leads to an elegant formulation of Al'Brekht's approximation algorithm. The sequence of large linear systems that arise are solved using an nWay version of the Bartels-Stewart algorithm for modest system dimension with low single digit polynomial degrees for the control law. We demonstrate this algorithm on a few test problem
Wildfires can pose threats to life, property and critical infrastructure, but wildland fire is an unavoidable part of many ecosystems. Improving our ability to cope with wildfires and avoiding catastrophic fire scenarios requires better understand how they interact with their surrounding environment.
The framework of port-Hamiltonian systems is a modeling paradigm and aims for a structured modeling approach that, on the one hand, is close to physics and, on the other hand, is particularly useful when it comes to mathematical analysis, approximation, simulation, an
Abstract: In this work, we consider a novel inverse problem in mean-field games (MFG).
To transform our lives, robots need to interact with other agents in complex shared environments. For example, autonomous cars need to interact with pedestrians, human-driven cars, and other autonomous cars. Autonomous delivery drones need to navigate in the aerial space shared by other drones, or mobile robots in a warehouse must navigate in the factory space shared by robots and humans.
